Membranes having good flexibility and resilience as well as excellent fluid (gas or liquid) barrier properties are needed for constructing gas-filled bladders, cushioning devices, and similar structures. The membranes need to have low gas transmission rates for nitrogen or other gases that are used to inflate the bladder or cushioning device. Thermoset and thermoplastic polymers are used in these applications because of their excellent flexibility. Thermoplastic polymers, particularly thermoplastic polyurethanes (“TPUs”), are desirable because their scraps can be reclaimed, melted, and reused to produce new thermoplastic articles. Although thermoset materials lack the recyclability advantage, they can be needed to achieve a well-balanced set of physical and mechanical properties for such demanding applications as footwear, sporting equipment, and automobile tires.